The present invention relates to a method for rapid carrier frequency estimation in a communication system.
Communication systems feature a transmitter and a receiver. In order for communication to occur, a transmitted signal must be accurately processed by the receiver for accurate recovery of the information contained within the signal.
For example, radio frequency signals are subject to distortion such as amplitude and phase distortion and carrier frequency offset. Amplitude and phase distortion, which cause time dispersion, are known as channel response. The transmission frame may include synchronization fields, which are required for correct processing of the frame to overcome the above-mentioned distortions, yet which must be minimized in order to maximize the available bandwidth. For example, for communication protocols which feature bursty transmissions, each burst may include synchronization fields. For example, these fields may appear at the beginning of the burst, and then they form the header. When bursts are relatively short, the synchronization overhead must be decreased as much as possible, such that the synchronization field must be as short as is practical.
Part of the processing of the synchronization field involves the estimation of the carrier frequency offset. The frequencies by which the signal are modulated, upconverted, downconverted and demodulated have some deviation from their ideal values. The sum of all these deviations is the carrier frequency offset. The estimation of the carrier frequency offset is necessary for processing the received signal. Methods for rapidly estimating the carrier frequency offset in the presence of channel distortion such as ISI (intersymbol interference) would therefore be very useful.
There is thus a widely recognized need for, and it would be highly advantageous to have, a system and a method for rapidly estimating the carrier frequency offset, in order to increase the efficiency of signal processing, and decrease the length of synchronization fields, and increasing the accuracy of the estimate.
According to the present invention there is provided a method for estimating a frequency offset of at least one frame, containing at least one synchronization field being divided into at least two subsections, the at least two subsections being composed of substantially equivalent pseudorandom symbols, the frame being received by a receiver from a transmitter, the receiver including at least an analog-to-digital processing unit, the steps of the method being performed by a data processor, the steps of the method comprising: (a) determining an initial frequency offset, finitial; (b) calculating a first phase in radians for at least a portion of a first subsection according to an equation:       ϕ    1    =      angle    ⁡          (                        ∑                      i            =                          i              m                                            i            n                          ⁢                  xe2x80x83                ⁢                              a            i            *                    *                      exp            ⁡                          (                                                -                  j                                *                i                *                                  f                  initial                                *                2                ⁢                                  xe2x80x83                                ⁢                π                *                                  T                  s                                            )                                ⁢                      Y            i                              )      
wherein i denotes time in symbols; Ts is a symbol period; n and m are integers, inxe2x89xa7im; a length of the at least a portion of the first subsection is inxe2x88x92im+1; Yi is an output of the analog-to-digital processing unit; ai* is the complex conjugate of the ith training symbol ai; (c) calculating a second phase in radians for at least a portion of a second subsection according to an equation:             ϕ      2        =          angle      ⁡              (                              ∑                          i              =                              i                p                                                    i              q                                ⁢                      xe2x80x83                    ⁢                                    a              i              *                        *                          exp              ⁡                              (                                                      -                    j                                    *                  i                  *                                      f                    initial                                    *                  2                  ⁢                                      xe2x80x83                                    ⁢                  π                  *                                      T                    s                                                  )                                      ⁢                          Y              i                                      )              ,
wherein q and p are integers, iqxe2x89xa7ip; a length of the at least a portion of the second subsection is iqxe2x88x92ip+1; (d) calculating a phase difference of the first phase and the second phase angle according to an equation: xcex94xcfx86=xcfx862xe2x88x92xcfx861; (e) adjusting the phase difference such that if xcex94xcfx86 greater than xcfx80, then xcex94xcfx86=xcex94xcfx86xe2x88x922xcfx80, and alternatively such that if xcex94xcfx86 less than xe2x88x92xcfx80, then xcex94xcfx86=xcex94xcfx86+2xcfx80; and (f) calculating the frequency offset according to an equation: xcex94f=xcex94xcfx86/(xcex94t*2xcfx80) wherein xcex94t=(ipxe2x88x92im)*Ts.
Preferably, the analog-to-digital processing unit features an analog-to-digital converter and Yi is an output of the analog-to-digital converter.
Alternatively and preferably, the analog-to-digital processing unit features a receive filter and Yi is an output of the receive filter.
According to a preferred embodiment of the present invention, the first subsection features three portions, a first symbol of a first portion being denoted i1, a first symbol of a second portion being denoted i2, a last symbol of the second portion being denoted symbol i3; and a last symbol for a third portion being denoted symbol i4; and wherein the second subsection features three portions, a first symbol of a first portion being denoted i5, a first symbol of a second portion being denoted i6, a last symbol of the second portion being denoted symbol i7; and a last symbol for a third portion being denoted symbol i8; such that the second portions of the first and the second subsections are processed, such that n=3, m=2, p=6 and q=7.
According to other preferred embodiments of the present invention, the steps of the method are repeated for a plurality of frames n, such that a plurality of n frequency offsets is calculated, the method further comprising the step of: (g) averaging the plurality of n frequency offsets to obtain the frequency offset. Preferably, the step of averaging the plurality of n frequency offsets includes the following steps: (i) determining a weight wi for each frequency offset i; and (ii) calculating the frequency offset to be xcex94fw according to an equation:       Δ    ⁢          xe2x80x83        ⁢          f      w        =            1                        ∑                      i            =            1                    n                ⁢                  xe2x80x83                ⁢                  w          i                      *                  ∑                  i          =          1                n            ⁢              xe2x80x83            ⁢              (                              w            i                    *          Δ          ⁢                      xe2x80x83                    ⁢                      f            i                          )            
Preferably, the initial frequency offset is calculated by the steps of: (i) calculating for each fk of a set of frequencies {fk} a set of values T(fk) according to an equation:       T    ⁡          (              f        k            )        =            "LeftBracketingBar"                        ∑                      i            =            1                    L                ⁢                  xe2x80x83                ⁢                              a            i                    *                      exp            ⁡                          (                                                -                  j                                *                i                *                                  f                  k                                *                2                ⁢                                  xe2x80x83                                ⁢                π                *                                  T                  s                                            )                                *                      Y            i                              "RightBracketingBar"        2  
wherein L is a length of the synchronization field; j is the square root of xe2x88x921; and (ii) determining the initial frequency offset as a value of a frequency fk such that the set of values T(fk) is maximized.
According to another embodiment of the present invention, there is provided a method for estimating a frequency offset of at least one frame, containing at least one synchronization field being divided into at least a first subsection and a second subsection separated by a spacer portion, the at least two subsections being composed of substantially equivalent pseudorandom symbols, the first subsection featuring at least three portions, a first portion having a first symbol denoted symbol i1, a second portion having a first symbol denoted symbol i2 and a last symbol denoted symbol i3, and a third portion having a last symbol denoted symbol i4, the second subsection also featuring at least three portions, a first portion having a first symbol denoted symbol i5, a second portion having a first symbol denoted symbol i6 and a last symbol denoted symbol i7, and a third portion having a last symbol denoted symbol i8, the frame being received by a receiver from a transmitter, the receiver including at least an analog-to-digital processing unit, the steps of the method being performed by a data processor, the steps of the method comprising: (a) calculating for each frequency fk of a set of frequencies {fk} an equation: T(fk)   =            "LeftBracketingBar"                        ∑                      i            =            1                    L                ⁢                  xe2x80x83                ⁢                              a            i                    *                      exp            ⁡                          (                                                -                  j                                *                i                *                                  f                  k                                *                2                ⁢                                  xe2x80x83                                ⁢                π                *                                  T                  s                                            )                                *                      Y            i                              "RightBracketingBar"        2  
wherein Ts is a symbol period; L is a length of at least a portion of the synchronization field; j is the square root of xe2x88x921; (b) determining an initial frequency estimate finitial as a value of a frequency fk such that a set of values T(fk) is maximized; (c) calculating a first phase in radians for the second portion of the first subsection according to an equation:       ϕ    1    =      angle    ⁡          (                        ∑                      i            =                          i              2                                            i            3                          ⁢                  xe2x80x83                ⁢                              a            i            *                    *                      exp            ⁡                          (                                                -                  j                                *                i                *                                  f                  initial                                *                2                ⁢                                  xe2x80x83                                ⁢                π                *                                  T                  s                                            )                                ⁢                      Y            i                              )      
wherein i denotes time in symbols; a length of the second portion of the first subsection is i3xe2x88x92i2+1; Yi is an output of the analog-to-digital processing unit; ai* is the complex conjugate of the ith symbol ai; (d) calculating a second phase in radians for the second portion of the second subsection according to an equation:       ϕ    2    =      angle    ⁡          (                        ∑                      i            =                          i              6                                            i            7                          ⁢                  xe2x80x83                ⁢                              a            i            *                    *                      exp            ⁡                          (                                                -                  j                                *                i                *                                  f                  initial                                *                2                ⁢                                  xe2x80x83                                ⁢                π                *                                  T                  s                                            )                                ⁢                      Y            i                              )      
wherein a length of the second portion of the second subsection is i7xe2x88x92i6+1; (e) calculating a difference of the first phase and the second phase according to an equation: xcex94xcfx86=xcfx862xe2x88x92xcfx861; (f) adjusting the difference such that if xcex94xcfx86 greater than xcfx80, then xcex94xcfx86=xcex94xcfx86xe2x88x922xcfx80, and alternatively if xcex94xcfx86 less than xe2x88x92xcfx80, then xcex94xcfx86=xcex94xcfx86+2xcfx80; and (g) calculating the frequency offset according to an equation: xcex94f=xcex94xcfx86/(xcex94t*2xcfx80) wherein xcex94t=(i6xe2x88x92i2)*Ts.
Hereinafter, a signal which corresponds to a particular burst Si (i being an integer) is defined as having been produced by processing at least a portion of burst Si, for example by sampling an analog signal obtained from the received burst Si to produce a xe2x80x9ccorrespondingxe2x80x9d digital sampled signal.